相依稳健t过程函数型ANOVA模型  

Dependent Robust Functional ANOVA Model with t Process

作　　者：张晨 王占锋[1] 吴耀华[1] ZHANG Chen;WANG Zhanfeng;WU Yaohua(Department of Statistics and Finance,University of Science and Technology of China,Hefei,230026,China)

机构地区：[1]中国科学技术大学统计与金融系,合肥230026

出　　处：《应用概率统计》2023年第1期73-92,共20页Chinese Journal of Applied Probability and Statistics

摘　　要：随着数据的多元化和复杂化,函数型ANOVA模型已经被越来越多的学者研究并应用到各行各业.为了减弱模型对于离群值的敏感度,本文对于相依的多元响应变量提出了一种相依稳健t过程函数型ANOVA模型.为了刻画变量之间的相依性和保证协方差函数的正定性,本文引入了随机效应变量和卷积方法构造了一个协方差函数.另外,模型中引入了随机效应函数去描述研究对象的个体特征.统计性质,例如稳健性和信息相合性在本文中也得到了相应的研究,并通过数值模拟和实例分析来验证此模型的可行性.With the diversification and complexity of data,functional ANOVA model has been studied by more and more scholars and applied to all walks of life.In order to reduce the sensitivity of the model to outliers,we figure out a dependent robust functional ANOVA model with t process for dependent multivariate response variables.To depict dependence between variables and ensure the positive definiteness of the covariance function,random effect variable and convolution method are introduced to construct a covariance function in this paper.In addition,the model introduces the random effect function to describe the individual characteristics of the research object.Statistical properties,such as robustness and information consistency,are also studied,and the feasibility of the model is verified by numerical simulation and example analysis.

关 键 词：相依函数型ANOVA模型 稳健性 

分 类 号：O212.7[理学—概率论与数理统计]